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The random paving property for uniformly bounded matrices

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Tropp J.

Studia Mathematica

2008

tom 185

nr 1

67-82

This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of Bourgain and Tzafriri involves a long, delicate calculation. The new proof relies on the systematic use of symmetrization and (noncommutative) Khinchin inequalities to estimate the norms of some random matrices.

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1 Studia Mathematica

1 Tropp J.

1 2008

Wyniki wyszukiwania

The random paving property for uniformly bounded matrices